Koskela, T., Varsta, M., Heikkonen, J., and Kaski, K. (1998). Time Series Prediction using Recurrent SOM with Local Linear Models. Int. J. of Knowledge-Based Intelligent Engineering Systems 2(1): 60-68.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....temporal information with the Self Organizing Map (SOM) with various successes. This includes both distributed and local types of representations. These methods use time delays [6, 11] recurrent connections [3, 4, 8] leaky integrators [1] or sometimes combine several of those principles [5, 9]. However, it is not clear in what sense these models correctly extend the SOM properties to time. In general, classical notions like vector quantization and quantization error are not adapted to their evaluation. In the present paper we present the Recursive Self Organizing Map, a SOM that ....

....order to evaluate how temporal information is stored in our model, it is therefore necessary to evaluate these immediate regularities, by comparison with a model that has no sensitivity to time. For this reason, we compared the Recursive SOM to the original SOM. We also included the Recurrent SOM [9] in our comparison, a temporal SOM that is Fig. 3. Comparison of the temporal receptive elds of the units of SOM (left) and Recursive SOM (right) Maps were trained on the Mackey Glass time series. The preferred input sequence of each unit is in black, with the most recent input on the left. The ....

T. Koskela, M. Varsta, J. Heikkonen, and K. Kaski. Time series prediction using recurrent SOM with local linear models. Int. J. of Knowledge-Based Intelligent Engineering Systems, 2(1):60-68, 1998.

.... processor (operator) In addition, neighboring units in the map are supposed to be sensitive to similar sequences (according to some similarity measure) In our approach, we employed leaky integrator SOM units, which were previously shown to be capable of topologically representing sequences [10,11]. The latter model [11] overcomes some limitations of the former and was also employed in our model. 2 The model Leaky integrating symbolic sequences with SOM formally corresponds to an Iterated Function System (IFS) introduced by Barnsley [12] IFS is defined by a collection of affine ....

.... In addition, neighboring units in the map are supposed to be sensitive to similar sequences (according to some similarity measure) In our approach, we employed leaky integrator SOM units, which were previously shown to be capable of topologically representing sequences [10,11] The latter model [11] overcomes some limitations of the former and was also employed in our model. 2 The model Leaky integrating symbolic sequences with SOM formally corresponds to an Iterated Function System (IFS) introduced by Barnsley [12] IFS is defined by a collection of affine contraction mappings i(s) s ....

T. Koskela et al. Time series prediction using recurrent SOM with local linear models. Int. Journal of Knowledge-Based Intell. Eng. Systems, 2:60--68, 1998.

....the TKM, the performance was obtained using a constant neighborhood associated with a decreasing learning rate, because this protocol gave better results in this case. that the representation of context learned by the TKM is limited to a restricted number of contexts. As shown by Koskela et al. [9], the weights learned by the units of a TKM converge towards linear combinations of the input patterns, explaining this restricted representation. In contrast, the receptive elds learned by the units of the RSOM ( gure 4.B) are able to represent any context, and the corresponding tree can develop ....

T. Koskela, M. Varsta, J. Heikkonen, and K. Kaski. Time series prediction using recurrent SOM with local linear models. Int. J. of Knowledge-Based Intelligent Engineering Systems, 2(1):60-68, 1998.

....cut from one side (Fig. 1) The model preserves the main features of the original SOM, that is, the processes of determining the winner, shrinking the neighborhood, and decreasing the learning rate, but uses a different, temporally enhanced model of the neuron. It is very similar to the RSOM model [11], which has been used for time series prediction. In the model, every neuron (i; j) has a Accepted to International Conference on Artificial Neural Networks (ICANN 99) Edinburgh, UK. Figure 1: The architecture of the visual cortex model. Every cortex neuron receives inputs from its receptive ....

T. Koskela, M. Varsta, J. Heikkonen, and K. Kaski. Time series prediction using recurrent SOM with local linear models. Int. Journal of Knowledge-Based Intelligent Eng. Systems, 2(1):60--68, 1998.

....in section 2. Classification of temporal sequences, clustering of EEG patterns and time series prediction are considered in section 3. Finally some conclusions are made. 2 Recurrent Self Organizing Map We present as an extension to the Self Organizing Map the Recurrent Self Organizing Map (RSOM) [17, 8] that allows storing certain information from the past input vectors. The information is stored in the form of difference vectors in the map units. The mapping that is formed during training has the topology preservation characteristic of the SOM. The Self Organizing Map (SOM) 6] is a vector ....

....Data Set Building RSOM vectors Local Models Local Model Prediction Select Local Model RSOM Training Local Model Estimation Figure 6: Construction of the local models. Figure 6. shows the procedure for building the RSOM models and evaluating their prediction abilities with testing data [8]. Time series is divided to training and testing data. Input vectors to RSOM are formed by windowing the time series. Free parameters during training for RSOM include input vector length p, time step between consecutive input vectors s, number of units n u and the leaking coefficient # of the ....

T. Koskela, M. Varsta, J. Heikkonen, and K. Kaski. Time series prediction using recurrent SOM with local linear models. Int. J. of Knowledge-Based Intelligent Engineering Systems, in press. Available as research reports B15, Helsinki University of Technology, Lab. of Computational Engineering, 1997.

....in section 2. Classification of temporal sequences, clustering of EEG patterns and time series prediction are considered in section 3. Finally some conclusions are made. 2 Recurrent Self Organizing Map We present as an extension to the SelfOrganizing Map the Recurrent Self Organizing Map (RSOM) [17, 8] that allows storing certain information from the past input vectors. The information is stored in the form of difference vectors in the map units. The mapping that is formed during training has the topology preservation characteristic of the SOM. The Self Organizing Map (SOM) 6] is a vector ....

....Data Local Data Set Building RSOM vectors Local Models Local Model Prediction Select Local Model RSOM Training Local Model Estimation Figure 6: Construction of the local models. Figure 6. shows the procedure for building the RSOM models and evaluating their prediction abilities with testing data [8]. Time series is divided to training and testing data. Input vectors to RSOM are formed by windowing the time series. Free parameters during training for RSOM include input vector length p, time step between consecutive input vectors s, number of units n u and the leaking coefficient ff of the ....

T. Koskela, M. Varsta, J. Heikkonen, and K. Kaski. Time series prediction using recurrent SOM with local linear models. Int. J. of Knowledge-Based Intelligent Engineering Systems, in press. Available as research reports B15, Helsinki University of Technology, Lab. of Computational Engineering, 1997.

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Koskela, T., Varsta, M., Heikkonen, J., and Kaski, K. (1998). Time Series Prediction using Recurrent SOM with Local Linear Models. Int. J. of Knowledge-Based Intelligent Engineering Systems 2(1): 60-68.

No context found.

T. Koskela, M. Varsta, J. Heikkonen, and S. Kaski, "Time series prediction using recurrent SOM with local linear models," International Journal of Knowledge-based Intelligent Engineering Systems, vol. 2, no. 1, pp. 60--68, 1998.

No context found.

T. Koskela, M. Varsta, J. Heikkonen, and K. Kaski, "Time series prediction using recurrent SOM with local linear models," International Journal of Knowledge-based Intelligent Engineering Systems, vol. 2, no. 1, pp. 60--68, 1998.

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